Building up spacetime with quantum entanglement

In this essay, we argue that the emergence of classically connected spacetimes is intimately related to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum gravity. Disentangling the degrees of freedom associated with two regions of spacetime results in these regions pulling apart and pinching off from each other in a way that can be quantified by standard measures of entanglement.Comment: Gravity Research Foundation essay, 7 pages, LaTeX, 5 figure

Growth of Inclined GaAs Nanowires by Molecular Beam Epitaxy: Theory and Experiment

The growth of inclined GaAs nanowires (NWs) during molecular beam epitaxy (MBE) on the rotating substrates is studied. The growth model provides explicitly the NW length as a function of radius, supersaturations, diffusion lengths and the tilt angle. Growth experiments are carried out on the GaAs(211)A and GaAs(111)B substrates. It is found that 20° inclined NWs are two times longer in average, which is explained by a larger impingement rate on their sidewalls. We find that the effective diffusion length at 550°C amounts to 12 nm for the surface adatoms and is more than 5,000 nm for the sidewall adatoms. Supersaturations of surface and sidewall adatoms are also estimated. The obtained results show the importance of sidewall adatoms in the MBE growth of NWs, neglected in a number of earlier studies

Representations of Double Affine Lie algebras

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the indecomposable modules to be irreducible, this is analogous to a result in the representation theory of quantum affine algebras. Finally, in the last section of the paper, we show, by using the notion of fusion product, that our modules are generically reducible

M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by grt_1, up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) E_n operads may be expressed through the cohomology of a suitable graph complex. Our methods also give a second proof of a result of H. Furusho, stating that the pentagon equation for grt_1-elements implies the hexagon equation

Mechanical Metamaterials with Negative Compressibility Transitions

When tensioned, ordinary materials expand along the direction of the applied force. Here, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension, and in response to this tension, is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilisations of (meta)stable equilibria of the constituents. These destabilisations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micro-mechanical controls, and protective devices.Comment: Supplementary information available at http://www.nature.com/nmat/journal/v11/n7/abs/nmat3331.htm

Genetic Analysis of Human Traits In Vitro: Drug Response and Gene Expression in Lymphoblastoid Cell Lines

Lymphoblastoid cell lines (LCLs), originally collected as renewable sources of DNA, are now being used as a model system to study genotype–phenotype relationships in human cells, including searches for QTLs influencing levels of individual mRNAs and responses to drugs and radiation. In the course of attempting to map genes for drug response using 269 LCLs from the International HapMap Project, we evaluated the extent to which biological noise and non-genetic confounders contribute to trait variability in LCLs. While drug responses could be technically well measured on a given day, we observed significant day-to-day variability and substantial correlation to non-genetic confounders, such as baseline growth rates and metabolic state in culture. After correcting for these confounders, we were unable to detect any QTLs with genome-wide significance for drug response. A much higher proportion of variance in mRNA levels may be attributed to non-genetic factors (intra-individual variance—i.e., biological noise, levels of the EBV virus used to transform the cells, ATP levels) than to detectable eQTLs. Finally, in an attempt to improve power, we focused analysis on those genes that had both detectable eQTLs and correlation to drug response; we were unable to detect evidence that eQTL SNPs are convincingly associated with drug response in the model. While LCLs are a promising model for pharmacogenetic experiments, biological noise and in vitro artifacts may reduce power and have the potential to create spurious association due to confounding

Genetical genomics: spotlight on QTL hotspots

No abstract available

The Individual and Synergistic Indexes for Assessments of Heavy Metal Contamination in Global Rivers and Risk: a Review

This article provides an overview of heavy metal contamination in rivers and assessment methods of their contamination and effects. According to literature, rivers with heavy metal contamination in surface water are mainly found in developing countries in Asia, Africa, and Latin America and the Caribbean area, while rivers with heavy metal contamination in sediments are mostly found in Europe. The increase in heavy metal contamination in rivers has led to the adoption of individual and synergistic assessment methods. Individual methods are useful in assessing the contamination and effects for a single heavy metal, while synergistic methods assess the combined contamination and effects of several heavy metals present in surface water and sediments. These two approaches have been commonly used together in recent studies to overcome the limitations of each other and provide a more comprehensive assessment. The developments, equations, advantages, limitations, and future perspectives of these methods are discussed in this review. Calculating indexes are simple, easy-to-implement, and effective methods to provide early alerts for the environmental changes and the adverse impacts on ecosystems and human health. However, calculating indexes still have limitations due to the lack of background concentrations of heavy metals in the study area. Therefore, this issue should be addressed to overcome the limitations of these methods in the future. This review provides a useful reference for future studies on heavy metal contamination in global rivers and the assessment methods for heavy metal contamination and effects

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144